**The Contraction Mapping Principle and Some Applications**

by Robert M. Brooks, Klaus Schmitt

**Publisher**: American Mathematical Society 2009**Number of pages**: 90

**Description**:

These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric and iterated function systems.

Download or read it online for free here:

**Download link**

(690KB, PDF)

## Similar books

**Ordinary Differential Equations**

by

**Dmitry Panchenko**-

**University of Toronto**

Contents: First order differential equations; Existence and uniqueness of solutions for first order differential equations; Systems of first order equations and higher order linear equations; Solving higher order linear differential equations; etc.

(

**6354**views)

**Nonlinear Analysis and Differential Equations**

by

**Klaus Schmitt, Russell C. Thompson**-

**University of Utah**

The intent of this set of notes is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions of solutions.

(

**13649**views)

**Periodic Solutions for Evolution Equations**

by

**Mihai Bostan**-

**American Mathematical Society**

We study the existence and uniqueness of periodic solutions for evolution equations. We analyze the one-dimensional case, then for arbitrary dimensions. We consider linear symmetric operators. We prove the same results for non-linear operators.

(

**9834**views)

**A First Course in Elementary Differential Equations**

by

**Marcel B. Finan**-

**Arkansas Tech University**

Contents: Basic Terminology; Qualitative Analysis: Direction Field of y'=f(t,y); Existence and Uniqueness of Solutions to First Order Linear IVP; Solving First Order Linear Homogeneous DE; Solving First Order Linear Non Homogeneous DE; etc.

(

**12091**views)